1、浙江大學(xué)理學(xué)院碩士學(xué)位論文代數(shù)多重網(wǎng)格法研究及在信號完整性分析系統(tǒng)中的應(yīng)用姓名：葉興會申請學(xué)位級別：碩士專業(yè)：計算數(shù)學(xué)指導(dǎo)教師：吳慶標(biāo)20070601代數(shù)多重網(wǎng)格法研究及在信號完整性分析系統(tǒng)中的應(yīng)用AbstractInthisthesisthealgebraicmultigridmethodisconsideredforsolvingsystemequationswhicharisefromafmiteelementdiscretiza

2、tionofpartialdifferentiaIequationsInparticularweconsidersystemequationsthatoriginatefiomalledgefiniteelementdisoretizationofMaxwell’sequationintimeandfiequencydomainwhichiswidelyusedinsignalintegrityanalysissystexas111eg

3、eneralalgebraicmethodismodifiedtofitthespecialmeshstructureweellcounterinpracticeandthenisusedasapreconditionerinseveralpreconditionedgrylovsubspaeemethodstosolvethesystemequationsinsignalintegrityanalysissystemefficient

4、lyInthemodifiedalgebraicmultigridmethodasthe3Dfiniteelementmeshiscomposedofseveral2Dfiniteelementmesheswhichhavethesamestructure，onlyone2DmeshneedtobecoarsenedTheconstructionofauxiliarymatricesandtheirprolongationoperato

5、rsisthesameasinthegeneralalgebraicmulti鰣dmethodButafterthesystemmatrixprolongationoperatorsbeingdefinedviathemethodproposedingeneralmulti鰣dmethodtheyhavetobeextendedtothe3DmeshAuxiliarymatricesandsystemmatricesonthecoars

6、cfllevel躺computedbytheGalerldnmethodasusualIIltllisthesissgveraIclassicaliterativemethodsaleintroducedsuchasGaussSeidelmethodconjugategradientmethodconjugategradientmethodforcomplexmatrices，BiCGmethodandBiCGSTABmethodPre

7、conditionedconjugategradientmethodandpreconditionedBiCGsl_ABmethodarcderivedfromtheconjugategradientmethodandBiCGSTABmethodBoththeAMGpreconditionedconjugategradientmethodandAMGpreconditionedBiCGSTABmethodcanefficientlyso

8、lvesystemequationsinthetimedomain111eformermayfailinthefrequencydomainbutthelaterisalsoallefficientsolverFinallynumericalstudiesarcgivenforproblemsinsignalintegrityanalysissystem碭ecoarsenedmeshesaregiveninfiguresSeverals